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## Quiz of the Month (April 2004)

### Hector C. Parr

***

#### SOLUTION TO LAST MONTH'S QUIZ

```  1.  3/4
2.  1/4
3.  1/3```

Notes

 Take x and y (each between 0 and 1) to represent the positions of the breaks, as shown. Then if we use x and y as the co-ordinates of a point in a unit square, we can illustrate ranges of values as regions within the square, and probabilities are represented by areas. The diagram represents the solution for Q.2. Because the longest piece is less than 0.5, each piece must be less than 0.5. ``` So if x < y we have: x < 0.5 AND y - x < 0.5 AND 1 - y < 0.5 and if y < x we have: y < 0.5 AND x - y < 0.5 AND 1 - x < 0.5``` The red regions represent this area, and the total area is 1/4.

#### THIS MONTH'S QUIZ

An aircraft, flying in a straight line at constant speed and height, passes over an observer on the ground.

1. When the aircraft is seen to be directly overhead its sound appears to come from a point 30o behind the aircraft. Taking the speed of sound as 1100 ft/sec, find the speed of the aircraft.

2. When the sound appears to come from directly overhead, find the angle between the vertical and the direction in which the aircraft is seen to be.

3. If it takes 5 seconds to fly from the point directly overhead to the point where the sound appears to come from directly overhead, find the height of the aircraft.

(c) Hector C. Parr (2004)

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